This is exactly the question that John Wentworth is trying to answer with his abstraction hypothesis framework.
Also related to Jaynes proof that probability of a fair coin coming up heads is 1⁄2.
As to being able to discern between different theories. Partly you are right that it can be hard during a scientific controversy and it involves a lot of judgement calls.
On the other hand, it can be hard for layman to appreciate how ‘rigid’ good mathematical models are.
Newton didn’t just observe that apples fall to the ground but he posited a series of elegant laws and was able to calculate very nonobvious results.
The entire theory is quite large and intricate—and there are many quantitive tests one can do and that have been done.
This is exactly the question that John Wentworth is trying to answer with his abstraction hypothesis framework. Also related to Jaynes proof that probability of a fair coin coming up heads is 1⁄2.
As to being able to discern between different theories. Partly you are right that it can be hard during a scientific controversy and it involves a lot of judgement calls. On the other hand, it can be hard for layman to appreciate how ‘rigid’ good mathematical models are. Newton didn’t just observe that apples fall to the ground but he posited a series of elegant laws and was able to calculate very nonobvious results. The entire theory is quite large and intricate—and there are many quantitive tests one can do and that have been done.